Questions: Davisson-Germer Experiment: Crystal Diffraction of Electrons

Question 1

In the Davisson-Germer experiment, why does electron intensity peak sharply at specific scattering angles rather than spreading diffusely in all directions?

• A. Electrons are repelled by the nickel crystal lattice except at specific angles where the crystal surface is smooth
• B. The electron beam is narrow and focused, so it only reaches the detector at specific angles
• C. Constructive interference occurs only when the path length difference between waves scattered from successive crystal planes equals a whole number of wavelengths (Bragg's law)
• D. The detector is only sensitive to electrons traveling in certain directions due to its geometry

Answer: (C)

The sharp peaks are the direct signature of wave interference. Electrons scatter from multiple parallel planes of the nickel crystal; the waves scattered from successive planes are only in phase (constructively interfering) when the path length difference between them satisfies Bragg's law: nλ = 2d sinθ. At all other angles, partial or complete destructive interference suppresses the signal. This peak-and-trough angular pattern is physically identical to what happens with X-rays or light waves in a diffraction grating — it requires a wave description and is impossible in classical particle physics.

Question 2

If electrons were purely classical particles with no wave properties, what would the Davisson-Germer experiment show?

• A. No electrons would scatter at all, since classical particles cannot penetrate a crystal
• B. Electrons would scatter with sharp peaks at angles predicted by Snell's law for refraction
• C. Electrons would scatter diffusely in all directions with no sharp angular dependence — a broad, smooth distribution
• D. Electrons would show diffraction peaks, but at different angles than de Broglie predicts

Answer: (C)

Classical particles bouncing off a crystal surface would scatter based on individual atomic collisions, producing a broad distribution that falls off gradually with angle — similar to billiard balls bouncing off a rough surface. There would be no reason for intensity to peak sharply at specific angles and drop to near-zero in between. The existence of dark regions (destructive interference) between sharp bright peaks is the unambiguous fingerprint of wave behavior. You cannot get a dark region from classical particles — they would simply scatter in that direction with some probability.

Question 3

The wavelengths measured from the Davisson-Germer diffraction patterns agreed quantitatively with de Broglie's prediction λ = h/p calculated from the electron's momentum.

• T. True
• F. False

Answer: True

The agreement was not merely qualitative. For electrons accelerated through 54 V, the momentum is p = √(2mₑeV) ≈ 4.0 × 10⁻²⁴ kg·m/s, giving λ = h/p ≈ 0.166 nm. The observed diffraction peak at about 50° from the nickel crystal (lattice spacing d ≈ 0.215 nm) is quantitatively consistent with this wavelength via Bragg's law. The match was at the percent level — not an order-of-magnitude agreement but a precise quantitative confirmation that de Broglie's formula was correct.

Question 4

The Davisson-Germer experiment showed that electrons sometimes behave as waves and sometimes as particles, depending on whether they are being measured.

• T. True
• F. False

Answer: False

This is a common misstatement of wave-particle duality. The Davisson-Germer experiment did not show context-dependent behavior — it showed that in this specific experimental context (diffraction from a crystal), electrons exhibit wave behavior. The experiment is a demonstration that matter waves are real, not a demonstration of observer-dependent collapse or context switching. The 'sometimes wave, sometimes particle' framing conflates the philosophical interpretation of quantum mechanics with the experimental result. The result is simply: electrons produce diffraction patterns consistent with λ = h/p, which requires a wave description.

Question 5

Why do sharp diffraction peaks rule out a classical (particle-only) explanation for the Davisson-Germer results?

Model answer: Sharp peaks at specific angles separated by regions of near-zero intensity are the hallmark of wave interference. Constructive interference (peaks) occurs only when waves from successive crystal planes are in phase, satisfying Bragg's law. Between these angles, destructive interference suppresses intensity. Classical particles have no mechanism for cancellation — two particles traveling in the same direction don't cancel each other out. A classical particle model predicts diffuse, angle-independent scattering from atomic collisions, not sharp peaks and dark troughs. The existence of the dark troughs (near-zero intensity between peaks) is the decisive evidence that electrons must behave as waves.

This reasoning is more powerful than just 'the peak positions match de Broglie' — it is the pattern of peaks AND troughs together that requires a wave description. X-rays, water waves, and light all produce the same pattern when scattered from periodic structures, and in each case the dark regions are the conclusive signature of wave cancellation. Davisson-Germer placed electrons unambiguously in this category.